The invention herein described was made in the course of or under a contract or subcontract thereunder, (or grant) with the Department of the Air Force. The invention relates to a circuit for transforming to polar coordinate form first and second binary number electrical signals representative of rectangular coordinates (quadrature components) for a vector or phasor. The first binary number electrical signal is representative of a coordinate dimension parallel to one axis of a two-dimensional rectangular coordinate system and the second binary number electrical signal is representative of a coordinate dimension parallel to the other axis of the two-dimensional rectangular coordinate system. The coordinate transforming circuit generates a third binary number electrical signal representative of the polar coordinate angle, measured relative to the one axis and determined by the magnitudes of the first and second binary number electrical signals. Once the third binary number electrical signal representative of the polar coordinate angle is generated, then the amplitude of the corresponding vector or phasor may be determined where required in the application of the coordinate transformation circuit.
In digital transmission and receiving systems, a transmitted carrier wave may be amplitude modulated, frequency modulated, phase modulated or, in the case of digital data transmission, frequency-shift keying or phase-shift keying may be utilized. The digital receiver of the modulated carrier wave must demodulate the wave to reconstruct the transmitted information. This may be accomplished by obtaining amplitude samples of the received waveform at a sampling rate of, for example, 230.4 kHz. The amplitude of the samples may be in the form of binary number electrical signals that can be multiplied by cosine and sine functions to produce binary number electrical signals representing the real (Re) and imaginary (Im) components of a phasor. If desired, the real and imaginary components may be filtered, translated in frequency or otherwise modified. The result is two streams of binary number samples, one stream representing the real components and the other the imaginary components of samples obtained from the received signal. The stream of real and imaginary components is demodulated to reconstruct the transmitted information. The circuit for transforming rectangular coordinate binary number electrical signals to polar coordinate binary number electrical signals is particularly suitable for use in the demodulation of the real and imaginary sample components derived from a received waveform, but the circuit and the principles embodied therein may be utilized in other applications as well.
With respect to the prior art, U.S. Pat. No. 3,648,041 to Beatrice describes an electronic angle generator in the form of an analogue circuit that transforms two voltages representative of two orthogonal components to a voltage having a magnitude proportional to the arctangent or the ratio of the two voltages Digital demodulation systems are described in U.S. Pat. Nos. 3,501,701 to Reid, 3,548,328 to Breikss, 3,600,680 to Maniere et al., 3,609,555 to VanBlerkom et al., 3,624,528 to Adkhock et al., 3,628,165 to Swan, Jr., and 3,670,250 to Fritkin. Of these patents, the Beatrice patent appears to be the most pertinent to the present invention.